The Q-depth relation in the earth's mantle has been estimated for long-period P waves from two deep-focus and three intermediate earthquakes. The amplitude spectrums of the first P waves from 114 seismograms at recording stations in the distance range between 15 and 103 degrees, have been corrected for the crustal structure and the instrument and used to measure the effects of attenuation over the whole mantle. Probable Q models are presented on the basis of the spectral amplitude ratios between these stations. The low Q between 120 and 280 in the upper mantle shows a rapid increase at depths around 900km to several thousands or greater in the lower mantle, and there is an apparent drop of Q near the base of the mantle. The frequency dependence of the spectral ratios against epicentral distance over about 80 degrees differs for the deep-focus and intermediate earthquakes, suggesting the possible diffraction effects due to the core